Matroid Theory with Graph Theory, Need an Introduction Book

Question

I am looking for a undergraduate introduction to matroid theory. We got them introduced today, to prove the Kruskal algorithm.... I can't say it was more elegant then the direct proof of the algorithm. I also do not see any benefits. Could maybe some explain why matroids are "great", my prof was very very fond of matroids.
I am also looking for an introduction book, maybe with exercises and solutions. (Russian, English, and German are okay.)

Answer 1

Most standard matroid theory texts feature graphic matroids as examples. James Oxley's survey paper ''What is a matroid?'' is a great starting place to learn about matroids, and has exercises. For more beyond that paper, Oxley's text Matroid Theory is the standard modern reference.

If you're interested particularly in optimization, it is a theorem that matroids are exactly the structures for which the greedy algorithm "works" (just as in Kruskal's algorithm).

Answer 2

Matroids: a geometric introduction by Gordon, McNulty was a good starting point for me.